Stabilizer R\'enyi entropy of 3-uniform hypergraph states
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Quantum Physics arXiv:2602.23687 (quant-ph) [Submitted on 27 Feb 2026] Title:Stabilizer Rényi entropy of 3-uniform hypergraph states Authors:Daichi Kagamihara, Shunji Tsuchiya View a PDF of the paper titled Stabilizer R\'enyi entropy of 3-uniform hypergraph states, by Daichi Kagamihara and 1 other authors View PDF HTML (experimental) Abstract:Nonstabilizerness, also known as magic, plays a central role in universal quantum computation. Hypergraph states are nonstabilizer generalizations of graph states and constitute a key class of quantum states in various areas of quantum physics, such as the demonstration of quantum advantage, measurement-based quantum computation, and the study of topological phases. In this work, we investigate nonstabilizerness of 3-uniform hypergraph states, which are solely generated by controlled-controlled-Z gates, in terms of the stabilizer Rényi entropy (SRE). We find that the SRE of 3-uniform hypergraph states can be expressed using the matrix rank, which reduces computational cost from $\mathcal{O}(2^{3N})$ to $\mathcal{O}(N^3 2^{N})$ for $N$-qubit states. Based on this result, we exactly evaluate SREs of one-dimensional hypergraph states. We also present numerical results of SREs of several large-scale 3-uniform hypergraph states. Our results would contribute to an understanding of the role of nonstabilizerness in a wide range of physical settings where hypergraph states are employed. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.23687 [quant-ph] (or arXiv:2602.23687v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.23687 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Daichi Kagamihara [view email] [v1] Fri, 27 Feb 2026 05:37:52 UTC (62 KB) Full-text links: Access Paper: View a PDF of the paper titled Stabilizer R\'enyi entropy of 3-uniform hypergraph states, by Daichi Kagamihara and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)